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Ramanujan Complexes of Type $\tilde{A_d}$

Representation Theory 2007-05-23 v2 Group Theory

Abstract

We define and construct Ramanujan complexes. These are simplicial complexes which are higher dimensional analogues of Ramanujan graphs. They are obtained as quotients of the buildings of type A~d1\tilde{A}_{d-1} associated with PGLd(F)\operatorname{PGL}_d(F) where FF is a local field of positive characteristic.

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Cite

@article{arxiv.math/0406208,
  title  = {Ramanujan Complexes of Type $\tilde{A_d}$},
  author = {Alex Lubotzky and Beth Samuels and Uzi Vishne},
  journal= {arXiv preprint arXiv:math/0406208},
  year   = {2007}
}

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32 pages